Extrude Solid up to surface

Hey there,

I want to develop a stair along a curve. The width is limited from two lofts, one each side and the depth should end when te next step starts. I set a box in the center of each step. For the depth I set a plane where the step should end. My question is if I can extrude this box until the next surface? The operators I know only enable to extrude along a vecor etc and evenly. Thanks for your help!